I stuffed my grandmother's slow cooker full of carrot sticks standing vertically, and slid thin slices of fresh ginger in between. Chunks of apple filled the remaining space, and it simmered overnight. After cooling, I put the still-firm carrots into a blender until smooth. After simmering the puree again, I added thyme, and served with shredded cheese sprinkled on top.
Very nice, but it didn't taste anything like carrot at all.